Total Rows: 34567
Total Columns: 61
INFO 523 - Project 1
The project investigates the intricate dynamics between childcare costs, unemployment rates, and poverty levels across various regions in the United States. Utilizing two primary datasets—the National Database of Childcare Prices (NDCP) and a comprehensive Counties Dataset—the analysis employs spatial mapping techniques to visualize mean unemployment rates and family poverty rates, as well as correlations between unemployment rates and poverty levels at the county and state levels. The findings reveal significant regional variations in unemployment rates, highlighting gender disparities, and underscore the correlation between unemployment rates and poverty levels. Furthermore, the project identifies regions with elevated family poverty rates and explores the relationship between family poverty rates and cumulative childcare costs. The results emphasize the economic challenges faced by families, especially in areas where childcare expenses intersect with high poverty rates. The project concludes with insights into future trends and the potential for integrating predictive modeling techniques and qualitative research methods to inform more effective policy interventions aimed at supporting families across the nation.
The United States faces persistent challenges related to childcare affordability, unemployment rates, and poverty levels, which have profound implications for family well-being and economic stability. Understanding the complex interplay between these factors is crucial for policymakers, researchers, and practitioners seeking to develop effective interventions to support families and communities.
This project aims to investigate the multifaceted relationship between childcare costs, unemployment rates, and poverty levels across diverse regions in the United States. Two primary datasets are utilized: the National Database of Childcare Prices (NDCP), providing comprehensive childcare price data spanning from 2008 to 2018, and a Counties Dataset offering geographical and demographic insights.
The analysis approach involves utilizing spatial mapping techniques to visualize mean unemployment rates, family poverty rates, and correlations between unemployment rates and poverty levels at both the county and state levels. By leveraging these datasets and visualization methods, the project seeks to uncover regional disparities in unemployment rates, gender discrepancies, and the economic burden faced by families due to childcare expenses.
The insights generated from this investigation have the potential to inform policymakers, researchers, and stakeholders about the socio-economic challenges faced by families across different regions of the United States. By understanding these dynamics, policymakers can develop targeted interventions to alleviate economic hardships and promote greater equity and prosperity for families nationwide.
Analyze factors affecting childcare costs across counties and predict high-cost regions.
Total Rows: 34567
Total Columns: 61
Removed the unwanted rows by removing all NA and error data.
Data Exploration
Rows: 23,342
Columns: 61
$ county_fips_code <int> 1001, 1001, 1001, 1001, 1001, 1001, 1001, 10…
$ study_year <int> 2008, 2009, 2010, 2011, 2012, 2013, 2014, 20…
$ unr_16 <dbl> 5.42, 5.93, 6.21, 7.55, 8.60, 9.39, 8.50, 7.…
$ funr_16 <dbl> 4.41, 5.72, 5.57, 8.13, 8.88, 10.31, 9.18, 8…
$ munr_16 <dbl> 6.32, 6.11, 6.78, 7.03, 8.29, 8.56, 7.95, 6.…
$ unr_20to64 <dbl> 4.6, 4.8, 5.1, 6.2, 6.7, 7.3, 6.8, 5.9, 4.4,…
$ funr_20to64 <dbl> 3.5, 4.6, 4.6, 6.3, 6.4, 7.6, 6.8, 6.1, 4.6,…
$ munr_20to64 <dbl> 5.6, 5.0, 5.6, 6.1, 7.0, 7.0, 6.8, 5.9, 4.3,…
$ flfpr_20to64 <dbl> 68.9, 70.8, 71.3, 70.2, 70.6, 70.7, 69.9, 68…
$ flfpr_20to64_under6 <dbl> 66.9, 63.7, 67.0, 66.5, 67.1, 67.5, 65.2, 66…
$ flfpr_20to64_6to17 <dbl> 79.59, 78.41, 78.15, 77.62, 76.31, 75.91, 75…
$ flfpr_20to64_under6_6to17 <dbl> 60.81, 59.91, 59.71, 59.31, 58.30, 58.00, 57…
$ mlfpr_20to64 <dbl> 84.0, 86.2, 85.8, 85.7, 85.7, 85.0, 84.2, 82…
$ pr_f <dbl> 8.5, 7.5, 7.5, 7.4, 7.4, 8.3, 9.1, 9.3, 9.4,…
$ pr_p <dbl> 11.5, 10.3, 10.6, 10.9, 11.6, 12.1, 12.8, 12…
$ mhi_2018 <dbl> 58462.55, 60211.71, 61775.80, 60366.88, 5915…
$ me_2018 <dbl> 32710.60, 34688.16, 34740.84, 34564.32, 3432…
$ fme_2018 <dbl> 25156.25, 26852.67, 27391.08, 26727.68, 2796…
$ mme_2018 <dbl> 41436.80, 43865.64, 46155.24, 45333.12, 4427…
$ total_pop <int> 49744, 49584, 53155, 53944, 54590, 54907, 55…
$ one_race <dbl> 98.1, 98.6, 98.5, 98.5, 98.5, 98.6, 98.7, 98…
$ one_race_w <dbl> 78.9, 79.1, 79.1, 78.9, 78.9, 78.3, 78.0, 77…
$ one_race_b <dbl> 17.7, 17.9, 17.9, 18.1, 18.1, 18.4, 18.6, 18…
$ one_race_i <dbl> 0.4, 0.4, 0.3, 0.2, 0.3, 0.3, 0.4, 0.4, 0.4,…
$ one_race_a <dbl> 0.4, 0.6, 0.7, 0.7, 0.8, 1.0, 0.9, 1.0, 0.8,…
$ one_race_h <dbl> 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.1,…
$ one_race_other <dbl> 0.7, 0.7, 0.6, 0.5, 0.4, 0.7, 0.7, 0.9, 1.4,…
$ two_races <dbl> 1.9, 1.4, 1.5, 1.5, 1.5, 1.4, 1.3, 1.6, 2.0,…
$ hispanic <dbl> 1.8, 2.0, 2.3, 2.4, 2.4, 2.5, 2.5, 2.6, 2.6,…
$ households <int> 18373, 18288, 19718, 19998, 19934, 20071, 20…
$ h_under6_both_work <int> 1543, 1475, 1569, 1695, 1714, 1532, 1557, 13…
$ h_under6_f_work <int> 970, 964, 1009, 1060, 938, 880, 1191, 1258, …
$ h_under6_m_work <int> 22, 16, 16, 106, 120, 161, 159, 211, 109, 10…
$ h_under6_single_m <int> 995, 1099, 1110, 1030, 1095, 1160, 954, 883,…
$ h_6to17_both_work <int> 4900, 5028, 5472, 5065, 4608, 4238, 4056, 40…
$ h_6to17_fwork <int> 1308, 1519, 1541, 1965, 1963, 1978, 2073, 20…
$ h_6to17_mwork <int> 114, 92, 113, 246, 284, 354, 373, 551, 322, …
$ h_6to17_single_m <int> 1966, 2305, 2377, 2299, 2644, 2522, 2269, 21…
$ emp_m <dbl> 27.40, 29.54, 29.33, 31.17, 32.13, 31.74, 32…
$ memp_m <dbl> 24.41, 26.07, 25.94, 26.97, 28.59, 27.44, 28…
$ femp_m <dbl> 30.68, 33.40, 33.06, 35.96, 36.09, 36.61, 37…
$ emp_service <dbl> 17.06, 15.81, 16.92, 16.18, 16.09, 16.72, 16…
$ memp_service <dbl> 15.53, 14.16, 15.09, 14.21, 14.71, 13.92, 13…
$ femp_service <dbl> 18.75, 17.64, 18.93, 18.42, 17.63, 19.89, 20…
$ emp_sales <dbl> 29.11, 28.75, 29.07, 27.56, 28.39, 27.22, 25…
$ memp_sales <dbl> 15.97, 17.51, 17.82, 17.74, 17.79, 17.38, 15…
$ femp_sales <dbl> 43.52, 41.25, 41.43, 38.76, 40.26, 38.36, 36…
$ emp_n <dbl> 13.21, 11.89, 11.57, 10.72, 9.02, 9.27, 9.38…
$ memp_n <dbl> 22.54, 20.30, 19.86, 18.28, 16.03, 16.79, 17…
$ femp_n <dbl> 2.99, 2.52, 2.45, 2.09, 1.19, 0.77, 0.58, 0.…
$ emp_p <dbl> 13.22, 14.02, 13.11, 14.38, 14.37, 15.04, 16…
$ memp_p <dbl> 21.55, 21.96, 21.28, 22.80, 22.88, 24.48, 24…
$ femp_p <dbl> 4.07, 5.19, 4.13, 4.77, 4.84, 4.36, 6.07, 7.…
$ mcsa <dbl> 80.92, 83.42, 85.92, 88.43, 90.93, 93.43, 95…
$ mfccsa <dbl> 81.40, 85.68, 89.96, 94.25, 98.53, 102.82, 1…
$ mc_infant <dbl> 104.95, 105.11, 105.28, 105.45, 105.61, 105.…
$ mc_toddler <dbl> 104.95, 105.11, 105.28, 105.45, 105.61, 105.…
$ mc_preschool <dbl> 85.92, 87.59, 89.26, 90.93, 92.60, 94.27, 95…
$ mfcc_infant <dbl> 83.45, 87.39, 91.33, 95.28, 99.22, 103.16, 1…
$ mfcc_toddler <dbl> 83.45, 87.39, 91.33, 95.28, 99.22, 103.16, 1…
$ mfcc_preschool <dbl> 81.40, 85.68, 89.96, 94.25, 98.53, 102.82, 1…
Total Rows: 23342
Total Columns: 61
Selecting only revelent column that need for project
We removed all rows where the study year is greater than 2015 due to the limited data available. This ensures more accurate analysis by focusing on years with sufficient data.
county_fips_code study_year unr_16 funr_16
Min. : 1001 Min. :2016 Min. : 0.000 Min. : 0.000
1st Qu.:21015 1st Qu.:2016 1st Qu.: 4.370 1st Qu.: 4.010
Median :37029 Median :2017 Median : 6.100 Median : 5.730
Mean :32996 Mean :2017 Mean : 6.436 Mean : 6.119
3rd Qu.:48004 3rd Qu.:2018 3rd Qu.: 7.990 3rd Qu.: 7.730
Max. :56045 Max. :2018 Max. :29.930 Max. :31.440
munr_16 mhi_2018 total_pop mc_infant
Min. : 0.000 Min. : 19842 Min. : 74 Min. : 53.58
1st Qu.: 4.420 1st Qu.: 42290 1st Qu.: 11205 1st Qu.:116.90
Median : 6.300 Median : 49351 Median : 27051 Median :144.96
Mean : 6.722 Mean : 51113 Mean : 107294 Mean :155.35
3rd Qu.: 8.390 3rd Qu.: 57094 3rd Qu.: 70291 3rd Qu.:175.00
Max. :39.740 Max. :136268 Max. :10105722 Max. :470.00
mc_toddler mc_preschool mfcc_infant mfcc_toddler
Min. : 49.39 Min. : 49.39 Min. : 47.56 Min. : 46.97
1st Qu.:110.00 1st Qu.:102.50 1st Qu.: 97.05 1st Qu.: 91.10
Median :130.69 Median :121.91 Median :112.50 Median :110.00
Mean :139.65 Mean :130.15 Mean :120.55 Mean :114.05
3rd Qu.:157.00 3rd Qu.:146.54 3rd Qu.:135.54 3rd Qu.:127.50
Max. :419.00 Max. :385.00 Max. :430.94 Max. :376.32
mfcc_preschool pr_f
Min. : 40.03 Min. : 0.00
1st Qu.: 90.00 1st Qu.: 7.60
Median :106.68 Median :10.60
Mean :111.19 Mean :11.57
3rd Qu.:125.00 3rd Qu.:14.30
Max. :331.34 Max. :52.10
Total Rows: 7384
Total Columns: 14
county_fips_code study_year unr_16 funr_16
0 0 0 0
munr_16 mhi_2018 total_pop mc_infant
0 0 0 0
mc_toddler mc_preschool mfcc_infant mfcc_toddler
0 0 0 0
mfcc_preschool pr_f
0 0
- Distribution of Childcare Costs (Infant, Toddler, Preschool):
- Boxplot of Unemployment Rates (unr_16, funr_16, munr_16):
'data.frame': 7384 obs. of 14 variables:
$ county_fips_code: int 1001 1001 1001 1003 1003 1003 1005 1005 1005 1007 ...
$ study_year : int 2016 2017 2018 2016 2017 2018 2016 2017 2018 2016 ...
$ unr_16 : num 5.59 5.21 4.23 6.29 5.5 ...
$ funr_16 : num 6.27 5.84 3.41 6.48 5.49 ...
$ munr_16 : num 4.99 4.64 4.93 6.12 5.52 ...
$ mhi_2018 : num 55754 56977 58786 53933 54139 ...
$ total_pop : int 55049 55036 55200 199510 203360 208107 26614 26201 25782 22572 ...
$ mc_infant : num 113 117 120 113 117 ...
$ mc_toddler : num 113 117 120 113 117 ...
$ mc_preschool : num 98.7 100.1 101.5 105.7 108.5 ...
$ mfcc_infant : num 107 107 107 106 107 ...
$ mfcc_toddler : num 107 107 107 106 107 ...
$ mfcc_preschool : num 107 106 106 106 107 ...
$ pr_f : num 9.4 10.9 12 9.3 8.2 7.3 20 20.5 21.5 11.7 ...
Purpose:
The numeric columns (unr_16, funr_16, etc.) are discretized into categorical bins using the cut() function. For example: Low: Bottom third of values. Medium: Middle third of values. High: Top third of values. The result is a dataset of categorical variables suitable for association rule mining.
Columns selected:
Unemployment rates (unr_16, funr_16, munr_16), median household income (mhi_2018), and total population (total_pop).
transactions as itemMatrix in sparse format with
7384 rows (elements/itemsets/transactions) and
15 columns (items) and a density of 0.3333333
most frequent items:
total_pop=Low munr_16=Low funr_16=Low unr_16=Low mhi_2018=Low
7372 7062 6769 6588 5796
(Other)
3333
element (itemset/transaction) length distribution:
sizes
5
7384
Min. 1st Qu. Median Mean 3rd Qu. Max.
5 5 5 5 5 5
includes extended item information - examples:
labels variables levels
1 unr_16=Low unr_16 Low
2 unr_16=Medium unr_16 Medium
3 unr_16=High unr_16 High
includes extended transaction information - examples:
transactionID
1 1
2 2
3 3
Apriori
Parameter specification:
confidence minval smax arem aval originalSupport maxtime support minlen
0.5 0.1 1 none FALSE TRUE 5 0.01 1
maxlen target ext
10 rules TRUE
Algorithmic control:
filter tree heap memopt load sort verbose
0.1 TRUE TRUE FALSE TRUE 2 TRUE
Absolute minimum support count: 73
set item appearances ...[0 item(s)] done [0.00s].
set transactions ...[15 item(s), 7384 transaction(s)] done [0.00s].
sorting and recoding items ... [9 item(s)] done [0.00s].
creating transaction tree ... done [0.00s].
checking subsets of size 1 2 3 4 5 done [0.00s].
writing ... [232 rule(s)] done [0.00s].
creating S4 object ... done [0.00s].
lhs rhs support confidence coverage lift count
[1] {funr_16=Medium,
munr_16=Medium} => {unr_16=Medium} 0.02153304 0.9695122 0.02221018 9.321456 159
[2] {funr_16=Medium,
munr_16=Medium,
total_pop=Low} => {unr_16=Medium} 0.02153304 0.9695122 0.02221018 9.321456 159
[3] {funr_16=Medium,
munr_16=Medium,
mhi_2018=Low} => {unr_16=Medium} 0.02126219 0.9691358 0.02193933 9.317837 157
[4] {funr_16=Medium,
munr_16=Medium,
mhi_2018=Low,
total_pop=Low} => {unr_16=Medium} 0.02126219 0.9691358 0.02193933 9.317837 157
[5] {munr_16=Medium} => {unr_16=Medium} 0.03819068 0.9126214 0.04184724 8.774474 282
[6] {munr_16=Medium,
total_pop=Low} => {unr_16=Medium} 0.03819068 0.9126214 0.04184724 8.774474 282
[7] {funr_16=Low,
munr_16=Medium} => {unr_16=Medium} 0.01665764 0.9111111 0.01828277 8.759954 123
[8] {funr_16=Low,
munr_16=Medium,
total_pop=Low} => {unr_16=Medium} 0.01665764 0.9111111 0.01828277 8.759954 123
[9] {munr_16=Medium,
mhi_2018=Low} => {unr_16=Medium} 0.03737811 0.9108911 0.04103467 8.757838 276
[10] {munr_16=Medium,
mhi_2018=Low,
total_pop=Low} => {unr_16=Medium} 0.03737811 0.9108911 0.04103467 8.757838 276
Available control parameters (with default values):
layout = stress
circular = FALSE
ggraphdots = NULL
edges = <environment>
nodes = <environment>
nodetext = <environment>
colors = c("#EE0000FF", "#EEEEEEFF")
engine = ggplot2
max = 100
verbose = FALSE


transactions as itemMatrix in sparse format with
7384 rows (elements/itemsets/transactions) and
15 columns (items) and a density of 0.3333333
most frequent items:
total_pop=Low munr_16=Low funr_16=Low unr_16=Low mhi_2018=Low
7372 7062 6769 6588 5796
(Other)
3333
element (itemset/transaction) length distribution:
sizes
5
7384
Min. 1st Qu. Median Mean 3rd Qu. Max.
5 5 5 5 5 5
includes extended item information - examples:
labels variables levels
1 unr_16=Low unr_16 Low
2 unr_16=Medium unr_16 Medium
3 unr_16=High unr_16 High
includes extended transaction information - examples:
transactionID
1 1
2 2
3 3
Eclat
parameter specification:
tidLists support minlen maxlen target ext
FALSE 0.01 1 5 frequent itemsets TRUE
algorithmic control:
sparse sort verbose
7 -2 TRUE
Absolute minimum support count: 73
create itemset ...
set transactions ...[15 item(s), 7384 transaction(s)] done [0.00s].
sorting and recoding items ... [9 item(s)] done [0.00s].
creating bit matrix ... [9 row(s), 7384 column(s)] done [0.00s].
writing ... [111 set(s)] done [0.00s].
Creating S4 object ... done [0.00s].
items support count
[1] {total_pop=Low} 0.9983749 7372
[2] {munr_16=Low} 0.9563922 7062
[3] {munr_16=Low, total_pop=Low} 0.9547671 7050
[4] {funr_16=Low} 0.9167118 6769
[5] {funr_16=Low, total_pop=Low} 0.9150867 6757
[6] {funr_16=Low, munr_16=Low} 0.8982936 6633
[7] {funr_16=Low, munr_16=Low, total_pop=Low} 0.8966685 6621
[8] {unr_16=Low} 0.8921993 6588
[9] {unr_16=Low, total_pop=Low} 0.8905742 6576
[10] {unr_16=Low, munr_16=Low} 0.8905742 6576

Available control parameters (with default values):
layout = stress
circular = FALSE
ggraphdots = NULL
edges = <environment>
nodes = <environment>
nodetext = <environment>
colors = c("#EE0000FF", "#EEEEEEFF")
engine = ggplot2
max = 100
verbose = FALSE


- Discretization:
The numeric columns are divided into "Low," "Medium," and "High" categories using cut().
- Transactions Conversion:
Convert the preprocessed data into a transaction format, required by arules.
- Eclat Algorithm:
eclat() generates frequent itemsets based on support.
Parameters:
supp = 0.01: Minimum support threshold (at least 1% of transactions must contain the itemset).
maxlen = 5: Maximum length of itemsets.
- Frequent Itemsets:
The output includes the most frequently occurring combinations of items.
- Visualization:
Item Frequency Plot: Displays the most frequent single items.
Graph-Based Visualization: Shows relationships among items within frequent itemsets.
Scatterplot: Highlights the support of frequent itemsets.
Visualizations
Top 10 Frequent Items:
Bar plot showing the frequency of the most common items.
Graph Plot:
A network plot where nodes represent items, and edges indicate their co-occurrence in frequent itemsets.
Scatterplot:
Displays itemsets by their support.
Medoids:
ID unr_16 funr_16 munr_16 mhi_2018 total_pop
[1,] 7384 1 1 1 1 1
[2,] 7383 1 1 1 2 1
[3,] 7092 2 2 1 1 1
Clustering vector:
[1] 1 1 2 1 1 1 3 3 1 1 1 1 1 1 1 3 3 3 1 1 1 3 3 1 1 1 1 1 1 1 1 1 1 3 1 3 3
[38] 3 3 1 1 1 1 1 1 1 1 1 1 1 1 3 3 3 3 3 1 3 3 1 1 1 1 1 1 1 3 3 1 3 3 3 1 1
[75] 1 1 1 2 3 3 3 1 1 1 1 1 1 3 1 1 3 1 1 3 3 3 3 3 3 1 1 1 1 1 1 1 1 1 1 1 1
[112] 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 3 3 3 3 2 2 2 3 3 3 1 1 1 1 1 1 1 1 1 3
[149] 3 3 1 1 1 1 1 1 3 3 3 3 3 3 3 3 1 1 1 1 1 1 1 1 1 1 2 2 2 3 3 3 3 3 1 1 1
[186] 3 1 1 1 3 3 1 3 3 1 3 3 3 1 3 1 2 2 2 3 3 3 1 1 1 1 1 1 3 3 3 3 3 1 3 3 2
[223] 3 3 1 1 2 2 3 3 1 3 3 3 1 1 1 1 1 1 3 3 3 1 1 1 3 3 3 1 1 1 3 3 1 1 1 1 2
[260] 2 2 1 1 1 3 3 3 1 1 1 1 1 1 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1
[297] 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[334] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 1 1 1 3 1 1 1 1 1 3 3 3 3 1 1 1
[371] 3 3 1 1 1 2 2 1 1 1 1 3 1 1 1 1 1 3 3 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[408] 1 3 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 1 2 2 2 3 3 3 1 1 1
[445] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 3 3 3 1 1 1 2 2 2 2 3 3 2
[482] 2 2 3 1 1 1 1 1 3 1 1 2 2 2 3 1 1 2 2 2 3 3 1 3 1 1 1 1 1 3 3 3 1 1 1 3 3
[519] 3 3 1 1 3 3 1 1 1 1 2 2 2 1 1 1 2 2 2 1 3 1 3 3 1 3 3 3 1 1 1 2 2 2 2 2 2
[556] 2 2 2 2 2 2 2 2 2 2 2 2 3 1 1 3 2 2 2 2 2 3 2 2 3 2 2 2 2 2 2 2 2 3 2 2 2
[593] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 3 1 1 2 2 2 2 2 2 3 3 3 3 3 1 3 3
[630] 1 1 1 1 3 3 1 3 1 1 2 2 2 2 2 2 3 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
[667] 2 2 2 2 2 2 1 2 2 2 2 2 1 2 2 1 1 1 2 1 1 3 1 1 1 1 1 3 1 3 1 3 1 2 2 2 2
[704] 3 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 3 1 3 1 3 3 3 1 3 3 1 1 3 3 3 1 3 3 1
[741] 1 3 3 1 1 1 1 1 1 1 1 1 1 3 1 1 1 3 1 1 1 1 1 2 2 2 2 2 2 3 1 1 1 1 1 1 2
[778] 1 1 1 1 1 1 3 3 2 2 1 1 2 2 1 1 2 2 1 1 3 1 1 1 1 1 1 2 1 1 1 3 1 1 1 1 1
[815] 1 1 1 1 3 3 1 1 3 2 1 1 1 3 3 1 3 1 3 1 3 3 2 1 3 3 3 2 1 1 2 1 2 1 3 1 2
[852] 1 1 3 3 3 2 1 1 2 1 3 1 1 2 1 2 1 2 1 1 1 1 3 1 2 1 1 3 3 2 1 3 2 1 1 1 1
[889] 1 3 1 3 1 3 3 1 2 3 1 3 3 1 3 1 3 1 3 3 1 3 1 1 1 1 3 3 2 1 2 3 2 1 3 3 1
[926] 3 3 1 1 3 3 3 1 3 3 3 3 3 1 3 1 3 1 3 3 1 3 1 1 3 1 1 1 3 1 1 1 3 3 3 1 3
[963] 1 1 1 1 1 1 2 2 2 2 2 2 3 1 3 1 1 1 1 1 1 3 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1
[1000] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1037] 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 1 1 1 1
[1074] 1 1 1 1 1 1 1 1 1 1 1 1 3 3 1 3 1 1 2 1 2 1 1 1 1 1 1 3 3 1 1 1 1 3 1 1 1
[1111] 1 1 2 2 2 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 1 1
[1148] 1 2 2 2 1 1 1 1 1 1 2 2 2 1 1 1 1 1 1 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1185] 3 1 1 1 1 1 1 1 1 1 1 1 2 2 2 1 1 1 1 1 1 3 3 3 1 1 1 1 1 1 1 1 1 1 1 1 2
[1222] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 1 1 1 2 2 2 1 1 1 2 2 2 1 1 1 1 1 1 1 2
[1259] 1 1 1 1 1 2 1 1 1 1 2 2 2 2 2 2 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1
[1296] 2 2 2 1 1 1 2 2 2 1 1 1 1 1 1 1 1 2 1 2 2 1 1 1 1 1 1 2 2 2 1 1 1 1 3 3 3
[1333] 3 1 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 3 3 1 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1370] 1 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 2 2 2 1 1 1 3 3 1
[1407] 2 2 2 1 1 1 1 1 2 1 2 2 2 1 1 1 1 1 2 1 1 1 1 1 1 1 1 2 1 1 2 1 2 2 1 1 1
[1444] 1 1 1 2 1 1 2 1 2 1 1 1 1 2 1 1 1 2 2 1 1 1 2 1 1 2 2 1 2 1 2 1 1 1 1 1 1
[1481] 1 1 1 2 1 2 1 1 1 1 2 1 2 1 1 1 1 1 1 2 2 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1
[1518] 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2
[1555] 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1592] 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 2 1 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1629] 1 1 1 2 1 1 1 1 1 2 2 2 1 1 1 2 2 2 1 1 1 2 2 1 1 1 1 1 1 1 2 1 1 2 2 2 1
[1666] 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 2 2 2 1 1 1 1 1 1 1 1 1 1 1
[1703] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 1 1 1 1 1 1
[1740] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 1 1 1 3 1 1 1 1 1 1
[1777] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 2 2 2 1 2 2 1 1 1 2 1
[1814] 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 2 2 2 1 1 1
[1851] 1 1 1 1 1 1 1 1 1 3 3 3 3 3 1 2 2 2 1 1 1 1 1 1 1 1 1 2 2 2 1 1 1 3 3 1 3
[1888] 3 1 1 1 1 3 1 1 1 1 1 3 1 3 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 3 3 3 1 1
[1925] 1 1 1 1 3 3 3 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1962] 1 1 1 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 3 1 1 1 1 1 1 3 1 3 2
[1999] 2 2 3 3 3 3 3 1 1 1 1 1 1 1 1 1 1 3 3 1 3 3 3 3 3 3 1 1 1 3 1 1 1 1 1 1 1
[2036] 1 1 1 1 1 1 1 3 3 3 1 1 1 1 1 1 3 3 3 1 1 1 1 1 1 3 3 3 1 1 1 1 1 1 3 1 1
[2073] 3 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 1 2 2 2 1 1 1 1 3 3 1
[2110] 1 1 3 3 3 3 3 1 1 1 1 1 1 1 1 1 1 3 3 1 1 1 1 3 1 1 2 2 2 2 2 2 1 1 1 2 2
[2147] 2 3 3 1 1 1 1 3 3 3 3 3 3 1 1 1 1 1 1 1 1 1 3 3 1 1 1 1 1 1 1 3 3 3 2 2 2
[2184] 1 1 2 1 3 1 3 1 1 1 3 2 1 3 3 3 1 3 1 3 3 1 3 1 1 1 1 1 1 1 3 2 3 1 3 1 1
[2221] 1 1 1 3 3 1 3 2 3 1 1 1 1 3 2 1 3 1 1 1 1 3 1 1 3 3 1 1 1 1 1 1 1 2 2 2 1
[2258] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 2 2 1 1 1 1 1 1 1 1 1 2 2
[2295] 2 1 1 1 2 2 2 2 2 2 2 2 2 1 1 1 2 2 2 2 2 2 2 2 2 3 1 1 2 2 2 1 1 1 2 2 2
[2332] 2 2 2 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 1 3 1 2 2 2 2 2 2 1 1 1 2 2 2 3 1 1 2
[2369] 2 2 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
[2406] 2 2 2 2 3 1 1 1 1 1 1 2 2 1 1 1 1 1 1 3 1 1 1 1 1 2 2 2 1 1 1 1 1 1 1 1 1
[2443] 1 1 1 1 1 1 1 1 1 1 1 1 3 3 1 3 1 1 3 3 3 2 2 2 3 3 1 1 1 1 1 1 1 2 2 2 1
[2480] 1 1 3 3 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1
[2517] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 3 3 3 1 1 2 2 2 2 1 1 1 2 2 2 3 3 1
[2554] 3 3 1 2 2 2 3 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 2 2 1 1 1 2 2 2 1 1 1 3 3 3 3
[2591] 1 1 1 1 1 2 2 2 1 1 1 3 3 1 3 3 1 1 1 1 3 3 3 1 1 1 2 2 2 3 3 1 3 3 3 1 1
[2628] 1 1 1 1 1 1 1 1 1 1 3 3 3 1 1 1 1 1 1 1 1 1 2 2 2 3 3 3 1 1 1 1 1 1 2 2 2
[2665] 1 1 2 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 1 1 1 1 2 1 2 2 2 2 2 2 1
[2702] 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 1 1 1 1 2 2 1 1 1 2 2 2 1 1 1 2 2
[2739] 2 1 1 2 1 1 1 2 2 2 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1
[2776] 2 2 2 1 1 1 1 1 1 2 2 2 3 1 1 2 2 2 1 1 1 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 2
[2813] 2 2 1 1 1 1 1 1 2 2 2 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 2 1 2 2 2 1 1 1 1 1
[2850] 1 1 1 1 2 2 2 1 1 2 1 1 2 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1
[2887] 1 1 1 1 1 1 2 2 2 1 1 1 1 1 1 2 2 2 1 1 1 1 1 1 1 2 2 2 1 1 1 3 3 3 1 1 1
[2924] 3 3 1 3 3 3 3 3 1 3 3 3 3 3 1 1 1 1 3 1 1 3 3 1 3 3 3 3 1 1 3 3 3 3 3 3 3
[2961] 3 3 3 3 3 2 2 2 3 3 3 3 3 1 1 1 1 3 3 3 1 3 1 1 1 1 1 1 1 3 1 1 3 3 3 3 3
[2998] 3 3 3 3 1 1 1 1 1 1 1 1 1 3 1 1 3 3 1 1 1 1 3 1 1 1 1 1 1 3 3 1 1 1 3 1 1
[3035] 1 1 3 1 1 1 3 3 3 1 1 1 3 3 3 2 2 2 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 3
[3072] 3 3 3 1 1 1 1 1 3 3 1 3 3 1 1 1 1 1 1 1 1 1 1 3 3 3 2 2 2 3 3 1 3 3 3 3 3
[3109] 3 1 1 1 1 1 1 3 3 3 3 3 3 1 1 1 3 1 1 3 3 3 3 3 3 1 1 1 1 1 1 1 1 1 3 3 3
[3146] 3 3 3 3 1 1 1 3 3 3 3 1 1 1 1 3 3 3 1 1 1 1 2 3 1 1 1 3 3 1 1 1 1 1 1 1 2
[3183] 1 1 1 1 2 1 3 1 1 1 2 1 1 2 1 3 1 1 1 1 1 1 1 1 1 3 1 1 1 1 2 1 1 1 1 1 2
[3220] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[3257] 1 1 1 1 1 1 1 2 2 2 1 2 2 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[3294] 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[3331] 1 1 1 1 1 2 2 2 1 1 1 1 1 1 1 1 1 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[3368] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 2 1
[3405] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 1 1 1 1 1 1 2 2 2 2
[3442] 2 2 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 1 1 1 2 2 2 1 1 1 1 1 1 1 1 1 2 2
[3479] 2 1 1 1 1 1 1 3 3 3 1 1 1 2 2 2 1 2 2 1 1 1 1 1 1 1 2 2 3 1 2 2 3 3 1 1 2
[3516] 2 2 1 2 2 2 2 2 2 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 3 3 2 2 2 2 2 2 2 2
[3553] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1
[3590] 3 1 1 1 1 1 1 1 2 1 1 2 1 1 1 1 2 1 3 1 1 1 1 1 2 1 1 2 2 1 1 2 2 2 1 1 1
[3627] 2 2 2 2 2 1 2 2 1 1 1 1 2 1 2 2 2 2 1 1 2 1 1 1 1 1 1 1 1 1 1 1 3 3 3 1 1
[3664] 1 1 1 1 1 1 1 3 3 3 3 1 1 1 1 1 1 1 1 3 1 1 2 2 2 3 1 1 2 2 2 1 1 1 1 1 1
[3701] 2 2 2 1 1 1 3 3 3 3 1 1 3 3 1 1 1 1 1 1 1 3 3 1 2 2 2 1 1 1 1 1 1 1 1 1 3
[3738] 1 1 1 1 1 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 3 1 1 1 1 1 1 1
[3775] 1 1 1 1 3 3 3 3 3 1 3 3 3 1 1 1 1 1 1 1 1 1 3 3 1 1 1 1 3 3 3 1 1 1 1 1 1
[3812] 1 1 1 1 1 1 3 3 3 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 1 3 3 1 2 2 2 1
[3849] 1 1 1 1 1 1 1 1 3 1 1 3 3 1 3 3 1 1 1 1 1 1 1 3 3 3 3 1 1 3 1 1 3 1 1 3 1
[3886] 1 1 3 1 3 3 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 2 2 2 3 3 1 2 2 2 1 1 1
[3923] 3 3 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2
[3960] 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 1 2 2 2 2 1 1 1 1 1 1 1 2 2 1 1 1 1 1
[3997] 1 1 1 1 1 1 1 1 1 1 2 2 1 2 2 2 1 2 1 2 2 2 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2
[4034] 2 2 2 1 1 1 2 2 2 2 2 2 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 1 1 1 2 2 2 1 1 1 3
[4071] 3 3 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 2 2 1 1 1 2 2 2 1 1 1 2 2 2 1 1 1 1 1
[4108] 1 1 1 1 1 1 1 1 1 1 2 2 2 1 1 1 1 1 1 2 2 2 1 1 1 1 1 1 1 1 1 2 2 2 1 1 1
[4145] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 1 1 1 2 2 2 1 1 1 1 1 2 2 2 2 1
[4182] 1 1 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 2 2 1 1
[4219] 1 3 3 3 1 1 1 1 1 1 2 2 2 1 1 1 2 2 2 1 1 1 1 1 1 1 1 1 2 2 2 1 1 1 1 1 1
[4256] 2 2 2 3 3 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[4293] 1 1 2 2 2 3 1 1 1 1 1 1 1 1 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 1 1
[4330] 1 1 1 1 1 1 1 1 1 1 2 2 2 1 1 1 3 3 1 2 2 2 1 1 1 1 1 1 1 1 1 2 2 2 1 1 1
[4367] 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 1 1 1 1 1 1 1 1 1 1
[4404] 1 1 2 2 2 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[4441] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2
[4478] 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 2 2 2 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1
[4515] 1 1 1 1 1 1 1 1 1 3 1 3 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[4552] 1 1 1 1 3 1 1 1 1 1 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 1 1 1
[4589] 1 1 1 2 2 1 2 2 2 1 1 1 1 1 2 2 2 2 1 1 1 1 2 2 3 1 1 3 1 1 3 1 1 1 2 2 3
[4626] 1 1 3 1 1 1 1 1 3 3 3 2 2 2 1 1 1 3 3 3 3 1 1 3 1 1 3 3 1 1 1 1 1 1 1 1 1
[4663] 1 1 1 1 1 1 1 1 1 1 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2
[4700] 3 1 1 1 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 1 1 1 1 1 1 2 2 2 2 2 2 1
[4737] 1 1 1 1 1 1 1 1 1 1 1 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 1 2 2 2 2
[4774] 2 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[4811] 2 2 2 1 1 1 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 1 1 1 2
[4848] 2 2 1 1 1 2 2 2 3 3 3 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[4885] 1 1 1 1 1 1 1 2 2 2 1 1 1 1 1 2 1 1 2 2 2 2 2 2 2 1 2 1 1 1 3 1 1 3 3 3 1
[4922] 1 1 1 1 1 3 3 1 2 2 2 1 1 2 1 1 1 1 2 2 1 1 1 3 1 1 3 1 3 3 3 3 3 1 1 3 3
[4959] 3 1 1 1 2 2 2 1 1 1 3 1 1 3 1 1 1 1 1 1 1 1 3 1 1 1 1 3 1 1 1 3 3 1 1 1 1
[4996] 1 1 1 1 1 1 3 1 1 1 2 2 3 3 3 3 3 3 3 3 3 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1
[5033] 1 1 1 1 1 3 3 3 3 1 1 3 1 1 2 2 2 1 2 2 1 1 1 3 3 3 1 1 1 1 1 1 1 1 1 1 1
[5070] 1 3 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 3 1 1 1 1 1 1 1 1 1 1 2 1
[5107] 3 3 3 1 1 1 2 2 2 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 2 2 2 1 1 1 2 2 2 1 1 1 2
[5144] 2 2 1 1 1 1 1 1 3 3 1 1 1 1 1 1 1 1 2 2 2 2 2 1 1 1 2 2 2 1 1 1 2 2 2 1 1
[5181] 1 1 2 2 1 1 2 3 1 1 1 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[5218] 1 1 1 2 2 2 2 2 2 3 3 3 1 1 1 1 1 1 2 2 2 1 1 1 1 1 1 3 3 3 1 1 1 1 1 1 3
[5255] 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 3 1 1 1 1 1 1 3 1
[5292] 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 1 1 1 1 1 1 1 1 1
[5329] 1 1 1 1 1 1 1 1 1 3 3 1 1 1 1 1 1 1 3 3 1 3 3 3 3 3 1 1 1 1 1 1 1 3 3 1 1
[5366] 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 3 3 1 3 1 1 1 1 1 1 1 1 1 1
[5403] 1 1 1 1 3 1 1 3 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 3 1 1 1 1 1 1 1 1
[5440] 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 3 1 1 3
[5477] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 3 2 2 1 1 1 3 3 1 1 1 1 3 3 3 1 1
[5514] 1 1 1 1 1 1 1 1 1 1 3 3 1 2 2 2 2 2 2 1 1 1 2 2 2 1 1 1 1 1 1 2 2 2 2 2 2
[5551] 1 1 1 2 2 2 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 1 1 1 1
[5588] 1 1 2 2 2 1 1 1 1 1 1 1 1 1 3 3 3 1 1 1 1 1 1 1 2 2 1 1 1 1 2 1 1 1 1 1 1
[5625] 1 1 1 1 2 2 2 1 1 1 1 1 1 2 2 2 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2
[5662] 3 3 3 1 1 1 2 2 2 1 1 1 1 1 1 2 2 1 1 3 3 3 3 3 2 2 2 1 1 1 3 3 1 1 1 1 1
[5699] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 1 1 1 3 3 3 3 3 3 1 1 1 3 3 3 1 1 1 2 2
[5736] 2 1 1 1 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 2 2 2 1 3 1
[5773] 1 1 1 1 1 1 2 2 2 2 2 2 1 1 1 1 1 1 2 2 2 3 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1
[5810] 1 1 2 2 2 1 1 1 1 3 3 1 1 1 1 1 1 1 1 1 1 1 2 1 2 2 1 1 1 2 2 2 3 1 3 2 2
[5847] 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1
[5884] 2 2 1 1 1 1 2 2 2 3 3 1 1 1 1 1 1 1 3 3 3 1 1 1 2 2 2 1 1 1 1 1 1 2 2 2 2
[5921] 2 2 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 3 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[5958] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 2 2 1 1 1 1 1 1 1 2 2 2 1 1 1 3 1 1 1 1 1
[5995] 1 1 1 2 3 2 1 1 1 1 3 3 2 2 2 1 1 1 1 1 1 3 3 3 2 2 2 1 1 1 2 2 2 3 1 1 1
[6032] 1 1 1 1 1 1 1 1 2 2 2 1 1 1 3 1 1 3 3 3 1 1 1 3 3 1 3 3 1 1 1 1 1 1 1 1 3
[6069] 1 1 2 2 1 1 1 1 1 1 1 1 1 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 2 2 2
[6106] 2 2 2 1 1 1 1 1 1 1 1 1 1 1 3 2 2 2 1 1 1 2 2 2 1 1 1 1 1 1 1 1 1 3 3 1 1
[6143] 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 3 1 3 3 1 1 1 1 1 1 1 1 1 3 3 3 1 1 1 1 1
[6180] 2 1 1 1 1 2 2 1 1 1 2 2 2 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 2 2 2 3 3 1
[6217] 3 1 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 1 1 1 1 1 1 1
[6254] 1 1 1 1 1 1 1 1 1 1 1 3 3 3 2 2 2 2 2 2 1 1 2 2 2 2 1 1 1 2 2 2 1 1 1 3 3
[6291] 3 3 3 1 1 1 1 1 2 2 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1
[6328] 1 2 2 1 1 1 1 2 2 2 2 2 1 1 1 1 1 1 2 2 2 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2
[6365] 2 2 2 2 2 2 2 2 1 1 1 1 1 1 2 2 2 2 2 2 1 1 1 1 1 1 2 2 2 1 1 1 2 2 2 2 2
[6402] 2 1 1 2 1 1 2 1 1 1 1 1 1 2 2 2 1 1 1 1 1 1 1 1 1 2 2 2 1 1 1 2 2 1 1 1 1
[6439] 1 1 1 2 2 2 2 2 2 1 1 3 2 2 2 1 1 1 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 1
[6476] 1 1 1 1 2 1 1 1 2 2 2 2 2 2 1 1 1 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2
[6513] 2 1 1 1 2 2 2 1 1 1 2 2 2 1 1 1 2 2 2 2 2 2 1 1 1 2 2 2 1 1 1 1 1 1 2 2 2
[6550] 2 2 2 1 1 1 1 1 1 2 2 2 2 2 2 1 1 3 2 2 2 2 2 2 1 1 1 3 3 3 2 2 2 1 2 2 1
[6587] 1 1 1 1 1 2 2 2 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 1 1 1 1 1 2 1 1 1 2 2 2 1 1
[6624] 1 1 1 1 1 1 1 2 2 2 1 1 1 2 2 2 2 2 2 1 1 1 2 2 2 1 1 1 2 2 2 1 1 1 1 2 2
[6661] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 2 2 2 1 1 1 1
[6698] 1 1 3 1 1 1 1 1 2 2 2 2 2 2 1 1 1 1 1 1 1 1 2 2 2 2 1 3 1 1 1 1 3 3 1 3 3
[6735] 3 2 2 2 2 2 2 3 3 3 1 2 2 1 1 1 1 1 1 1 1 1 3 3 1 1 1 1 1 1 1 2 2 2 2 2 2
[6772] 3 1 1 1 1 1 1 1 1 3 3 3 3 3 3 2 2 2 3 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2
[6809] 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 1 1 1 1 1 1 2 2 2 1 1 1 1 1
[6846] 1 1 1 2 1 1 1 2 2 2 1 1 1 1 1 1 3 3 1 2 2 2 1 1 1 2 2 2 2 2 2 1 1 1 1 1 1
[6883] 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 1 1 1 2 2 2 1 1 1 1
[6920] 1 1 2 2 2 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 2 2 2 1 3 1 3 3 3 1 1 1 1 1
[6957] 1 3 3 3 3 3 1 1 1 1 1 1 1 3 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[6994] 2 2 2 1 1 1 1 1 1 1 1 1 3 3 3 3 3 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 3 3 3 1
[7031] 1 1 1 1 1 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 1 1 1 1 1 1 1 1
[7068] 1 3 1 1 3 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 3 1 1 1 1 1 1 1 1 1 3 3 3
[7105] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 2 2 2 1 1 1 1 1 1 2 2 2 1 1 1 2
[7142] 2 2 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 1 1 1 2 2 2 1 1 1 2 2 2 1 1
[7179] 1 1 1 2 2 2 1 1 1 2 2 2 2 2 2 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1
[7216] 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 1 1 1 2 2 2 1 1 1 1 1 1 1 1 1
[7253] 2 2 2 1 1 1 1 1 1 1 1 1 2 2 2 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1
[7290] 1 1 1 2 2 1 1 1 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2
[7327] 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 1 1 1 2 2 2 1 1 1
[7364] 1 1 1 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 2 1
Objective function:
build swap
0.1099288 0.1099288
Available components:
[1] "medoids" "id.med" "clustering" "objective" "isolation"
[6] "clusinfo" "silinfo" "diss" "call" "data"
1 2 3
4887 1582 915


Explanation of Code: K-medoids Clustering:
Step 1: Discretize the numeric variables into categorical values.
Step 2: Convert the categorical columns to numeric values, which is required for clustering.
Step 3: Apply the pam() function, which performs K-medoids clustering, where k = 3 specifies the number of clusters.
Step 4: The result is visualized, and the clusters are added back to the original data for further inspection.
Plot Explanation:
Axes (Component 1 and Component 2):
These are the principal components resulting from a dimensionality reduction process like PCA (Principal Component Analysis) applied to your dataset.
Since your data likely has many variables, PCA simplifies the data into two components to visualize in a 2D space.
Clusters:
The different shapes (e.g., triangle, circle, cross) represent different clusters identified by the K-medoids algorithm.
Each shape corresponds to one of the three clusters (k = 3 in your case).
Ellipses:
The ellipses around the clusters show the spread or variability of data points within each cluster.
Tighter ellipses indicate that the points in the cluster are more compact and closely related.
Medoids (Cluster Centers):
The cluster centers (medoids) are the most representative data points within each cluster. They are marked by the shapes at the center of each cluster.
Pink Lines:
These lines connect data points to their respective medoids (cluster centers).
They indicate the assignment of each data point to its cluster.
Explained Variability:
The note at the bottom indicates that 64.61% of the variability in the dataset is explained by the two components plotted.
While this is a decent percentage, it suggests that there might be additional variability captured in higher dimensions not represented here.

1 2 3
4873 1590 921

Hierarchical Clustering:
Step 1: Discretize the numeric variables into categorical values.
Step 2: Convert the categorical columns to numeric values, which is required for clustering.
Step 3: Compute the distance matrix using dist() with Euclidean distance. This matrix is then used to perform hierarchical clustering using hclust().
Step 4: The dendrogram is plotted to visualize the hierarchical clustering. You can specify the number of clusters using cutree().
Step 5: Cluster labels are added to the dataset, and the clusters can be inspected